can someone simplify this?

Emurry, I was just looking at your answer. :)

1-y<|2x-1|

-y < -1 + |2x-1|

y > 1 - |2x-1|

this is different from your version.

-|2x-1|  is not equal to |-2x+1|

If you think about it for a moment you will realise that the first expression is negative and the second one is positive. :)

it might be y>|-2x+1|+1 correct me if you think other wise :)

1-y<|2x-1|

-(2x-1) < 1-y < 2x-1

-2x+1 < 1-y < 2x-1

-2x+1 -1 < 1-y -1 < 2x-1 -1

-2x < -y < 2x- 2

-2x < -y      and       -y < 2x- 2

2x > y      and       y > -2x+ 2

y<2x       and        -2x+ 2 < y

-2x+2 < y < 2x

This also means that  

-2x+2<2x

2 < 4x

1/2 < x

x > 0.5

I have not checked this answer - if you have questions please ask.

thanks I went back to notes and this helped 

It is really nice to meet you Emurry.

It is great when students demonstrate an active interest in learning from other people's answers :)

oh now i see :) thanks a lot

1-y<|2x-1|    rearrange as

y > 1 - l 2x - 1 l     this might best be answered by a graph

https://www.desmos.com/calculator/9hj3pnhecz

Notice that the answer to this problem is an area......not just a single value

This area  is everything "above" the area formed by the intersection of the lines  y = 2x and y =  -2x + 2 .........the lines themselves are not included